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Full text of "Mathematical And Physical Papers - Iii"

ON THE MOTION OF PENDULUMS.
89
gyration in order to express the effect of the inertia of the air, 8 the vibrating specific gravity of the pendulum, the effects of buoyancy and inertia are as crS'1 to ww~l\ hut they are also as 1 to tt — 1, according to the definition of the factor tt, and therefore
(155),
a formula which may be  employed to calculate -wr when n is known.
Baily's results with spheres at the end of long rods.
No. 45 — l-|-inch sphere with copper rod.						
No. 46 —2-inch sphere with ditto.						
No. 47 —3-inch sphere with ditto.						
No. 48 - 1 J-inch sphere with brass rod. No. 49 —2-inch sphere with ditto.						
No. 50 -3-inch sphere with ditto.						
No. 51 — l-|-inch sphere with steel rod.						
No. 52 — 2-inch sphere with ditto.						
No. 53 —3-inch sphere with ditto.						
	Value of n			Weight of adhesive air, in grains		
No.	By theory	By experiment	Difference	By theory	By experiment	Difference
45	2-525	2-458	-0-067, or -Jg-	4-863	4-564	-0-299, or -Jg-
46	2-202	2-234	+ 0-032, or +^-	5-005	5-076	+ 0-071, or +?L
47	1-957	1-873	-0-084, or -o^-	7-071	6-425	-0-646, or - jL
48	2-375	2-356	-0-019, or -~i-f	1-447	1-417	-0-030, or -^
49	2-060	1-982	-0-078, or -oV'	2-135	1-973	-0-162", or -r\.
50	1-631	1-933?	+ 0-302?	4-411	4-868 ?	+ 0-457?
51	2-099	2-344 ?	+ 0-245?	0-682	0-834?	+ 0-152?
52	1-920	1-793	-0-127, or -fL	1-457	1-259	-0-198, or --J
53	1-781	1-759	- 0-022, or - -^L	3-742	3-670	-0-072, or - J*
With respect to the two experiments marked ? Baily remarks, "These two experiments (with the pendulums Nos. 50 and 51) are very unsatisfactory; and are marked as such in my journal. It was consequently my intention to have repeated them ; but the subject was overlooked till it was too late. I should propose their being rejected altogether." If these two experiments be struck out, it will be seen that the differences between, theory and experiment are very small, especially when the difficulty of this set of experiments is considered, arising from the frequency of the coincidences with the mean solar clock.